A history of Greek mathematics Vol.II from Aristarchus to Diophantus by Heath, Thomas Little, Sir, 1921

approximations
=
ENGLISH INDEX 571
572 ENGLISH INDEX
Anthemius of Tralles 243, ii. 194,
ii. 200-3, ii. 518, ii. 540, ii.
541-3.
Antiphon 184, 219, 221-2. 224,
271.
A pastamba-Sulba-Sutra 145-6.
Apelt, E. F. 330.
Apelt, 0. 181 n., 182.
Apices 47.
Apollodorus, author of Chronica,
176.
Apollodorus 6 Xoyto-ruo? : distich of,
131.133, 134, 144, 145.
Apollonius of Perga ii. 1, ii. 126.
Arithmetic : axvroKiov 234, ii.
194, ii. 253 (approximation to
77, ib.), 'tetrads' 40, continued
multiplications 54-7.
Astronomy ii. 195-6: A. and
Tycho Brahe 317, ii. 196: on
epicycles and eccentrics ii. 195 6,
ii. 243 : trigonometry ii. 253.
Conies ii. 126-75: text ii. 126-
8, Arabic translations ii. 127,
prefaces ii. 128-32, characteristics
ii. 132-3: conies obtained
from oblique cone ii. 134-8,
prime property equivalent to
Cartesian equation (oblique axes)
ii. 139, new names, parabola, &c.
150, 167, ii. 138, transformation
of coordinates ii. 141-7, tangents
ii. 140-1, asymptotes ii. 148-9,
rectangles under segments of intersecting
chords ii. 152-3, harmonic
properties ii. 154-5, focal
properties (central conies) ii. 156—
and minima
7, normals as maxima
ii. 159-67, construction of
normals ii. 166-7, number of
normals through point ii. 163-4,
propositions giving evolute ii.
164-5.
On contacts ii. 181-5 (lemmas
to, ii. 416-17), three-circle problem
ii. 182-5.
Sectio rationis ii. 175 9 (lemmas
to, ii. 404-5).
Sectio spatii ii. 179-80, ii. 337.
ii. 339.
Determinate section ii. 180-1
(lemmas to, ii. 405-12).
Comparison of dodecahedron
and icosahedron 419-20, ii. 192.
Duplication of cube 262-3, ii.
194.
'General treatise 1 ii. 192-3, ii.
253 : on Book I of Euclid 358.
vcvaeis ii. 68, ii. 189-92 (lemmas
to, ii. 412 16), rhombus-problem
ii. 190-2, square - problem ii.
412-13.
Plane Lociii. 185-9 (lemmas to,
ii. 417-19).
On cochlias 232, ii. 193, sister
'
of cochloid' 225, 231-2, On irrationals
ii. 193, On the burningmirror
ii. 194, ii. 200-1.
Application of areas 150-3 : method
attributed to Pythagoras 150.
equivalent to solution of general
quadratic 150-2, 394-6.
Approximations to \/2 (by means
of side- and diameter ' ' -' numbers)
91-3, (Indian) 146 : to ^/3
'
(Ptolemy) 45, 62-3, (Archimedes)
ii. 51-2: to n 232-5, ii. 194, ii.
253 : to surds (Heron) ii. 323-6,
cf. ii. 547-9, ii. 553-4 : to cube
root (Heron) ii. 341-2.
Apuleius of Madaura 97, 99.
Archibald, R. C. 425 n.
Archimedes 3, 52, 54, 180, 199, 202,
203 w., 213, 217, 224-5, 229, 234,
272, ii. 1.
Traditions ii. 16-17, engines ii.
17, mechanics ii. 18, general
estimate ii. 19-20.
Works : character of, ii. 20-2,
works extant ii. 22-3, lost ii. 23-
5, 103 ; text ii. 25-7, MSS. ii. 26,
editions ii. 27 : The Method ii. 20,
21, 22, 27-34, ii. 246, ii. 317-18 :
On the Sphere and Cylinder ii. 34-
50 : Measurement of a circle ii. 50-
6, ii. 253 : On Conoids and Spheroids
ii. 56-64 : On Spirals 230-1,
ii. 64-75 (cf. ii. 377-9), ii. 556-61
Sand-reckoner ii. 81-5 : Quadrature
of Parabola ii. 85-91 : mechanical
works, titles ii. 23-4,
Plane equilibriums ii. 75-81 : On
Floating Bodies ii. 91-7, problem
of crown ii. 92-4 : Liber assumptorum
ii. 101-3: Cattle-problem
14, 15, ii. 23, ii. 97-8, ii. 447 :
Catoptrica 444, ii. 24.
Arithmetic : octacls 40-1, fractions
42, value of tv 232-3, 234,
ii. 50-6 : to \/%
ii. 51-2.
Astronomy ii. 17 18, sphere-
making ii. 18, on Aristarchus's
hypothesis ii. 3-4.
Conies, propositions in, 438-9,
ii. 122-6.
Cubic equation solved by conies
ii. 45-6.
On Democritus 180, 327,
equality of angles of incidence
and reflection ii. 353-4, integral
calculus anticipated ii. 41-2, 61.
62-3, 74, 89-90: Lemma or Axiom
of A. 326-8, ii. 35 : veuaeis in, ii.
65-8 (Pappus on, ii. 68) : on semiregular
solids ii. 98-101 : triangle,
area in terms of sides ii. 103
trisection of any angle 240-1.
Archytas 2, 170, 212-16, ii. 1 : on
/j.adr]fi(iTa 11, on logistic 14, on 1
as odd-even 71 : on means 85, 86:
no mean proportional between n
and n + 1, 90, 215: on music 214:
mechanics 213 : solution of problem
of two mean proportionals
214, 219, 245, 246-9, 334, ii. 261.
Argyrus, Isaac, 224 n., ii. 555.
Aristaeus : comparison of five regular
solids 420 : Solid Loci (conies)
438, ii. 116, 118-19
Aristaeus of Croton 86.
Aristarchus of Samos 43, 139, ii. 1-
15, ii. 251 : date ii. 2 : ovaic/^ of,
ii. 1 : anticipated Copernicus ii.
2-3: other hypotheses ii. 3, 4:
treatise On sizes and distances of
Sun and Moon ii. 1, 3, 4-15, trigonometrical
purpose ii. 5 : numbers
in, 39 : fractions in, 43.
Aristonophus, vase of, 162.
Aristophanes 48, 161, 220.
Aristotelian treatise on indivisible
lines 157, 346-8.
Aristotherus 348.
Aristotle 5, 120, 121 : on origin of
science 8: on mathematical subjects
16-17 : on first principles, definitions,
postulates, axioms 336-8.
Arithmetic : reckoning by tens
26-7, why 1 is odd-even 71 : 2
even and prime 73 : on Pythagoreans
and numbers 67-9 : on
the gnomon 77-8, 83.
Astronomy : Pythagorean system
164-5, on hypothesis of concentric
spheres 329, 335, ii. 244,
on Plato's view about the earth
314 15.
On the continuous and infinite
342-3 : proof of incommensurability
of diagonal 91 : on principle
of exhaustion 340 : on Zeno's
paradoxes 272, 275-7, 278-9, 282:
on Hippocrates 22 : encomium on
Democritus 176.
Geometry : illustrations from
335, 336, 338-40, on parallels
339, proofs differing from Euclid's
338-9, propositions not in Euclid
340, on quadratures 184-5, 221,
223, 224 n., 271, on quadrature
by lunes (Hippocrates) 184-5,
198-9 : on Plato and regular
solids 159 : curves and solids in
A. 341.
Mechanics 344- 6, 445- 6 : parallelogram
of velocities 346 : 'Aristotle's
wheel' ii. 347-8.
Aristoxenus 24 n. y
66.
Arithmetic (1
J = theory of numbers
(opp. to XoyioTiKrj) 13-16 : early
'
Elements of A rithmetic ' 90, 216
systematic treatises, Nicomachus
Introd. Ar. 97-112, Theon of
Smyrnall2-3,Iamblichus,Comm.
on Nicomachus 1 13-15, Domninus
ii. 538. (2) Practical arithmetic :
originated with Phoenicians 120-
1, in primary education 19-20.
Arithmetic mean, defined 85.
Arithmetica of Diophantus 15-16,
ii. 449-514.
Arithmetical operations: see Addition,
Subtraction, &c.
Arrow oi Zeno 276, 280-1.
Aryabhatta 234.
Asclepius of Tralles 99.
Astronomy in elementary education
19 : as secondary subject 20-1.
Athelhard of Bath, first translator
of Euclid 362-4.
Athenaeus 144, 145.
Athenaeus of Cyzicus 320-1.
•
Attic (or 'Herodianic') numeials
'
30-1.
August, E. F. 299, 302, 361.
Autolycus of Pitane 348 : works
On the moving Sphere 348-52, On
Risings and Settings 352-3 : relation
to Euclid 35 i -2.
Auverus, C. ii. 26.
Axioms : Aristotle on, 336 : Common
Notions in Euclid 376 : Axiom
of Archimedes 326-8, ii. 35.